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Periodic Bouncing Solutions for Nonlinear Impact Oscillators

Periodic Bouncing Solutions for Nonlinear Impact Oscillators Abstract We prove the existence of a periodic solution to a nonlinear impact oscillator, whose restoring force has an asymptotically linear behavior. To this aim, after regularizing the problem, we use phase-plane analysis, and apply the Poincaré-Bohl fixed point Theorem to the associated Poincaré map, so to find a periodic solution of the regularized problem. Passing to the limit, we eventually find the “bouncing solution” we are looking for. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advanced Nonlinear Studies de Gruyter

Periodic Bouncing Solutions for Nonlinear Impact Oscillators

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Publisher
de Gruyter
Copyright
Copyright © 2013 by the
ISSN
1536-1365
eISSN
2169-0375
DOI
10.1515/ans-2013-0110
Publisher site
See Article on Publisher Site

Abstract

Abstract We prove the existence of a periodic solution to a nonlinear impact oscillator, whose restoring force has an asymptotically linear behavior. To this aim, after regularizing the problem, we use phase-plane analysis, and apply the Poincaré-Bohl fixed point Theorem to the associated Poincaré map, so to find a periodic solution of the regularized problem. Passing to the limit, we eventually find the “bouncing solution” we are looking for.

Journal

Advanced Nonlinear Studiesde Gruyter

Published: Feb 1, 2013

References

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